A limiting case of a theorem of C. Miranda for layer potentials in Schauder spaces
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866914950839009280 |
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| author | de Cristoforis, Massimo Lanza |
| author_facet | de Cristoforis, Massimo Lanza |
| contents | The aim of this paper is to prove a theorem of C.~Miranda for the single and double layer potential corresponding to the fundamental solution of a second order differential operator with constant coefficients in Schauder spaces in the limiting case in which the open set is of class $C^{m,1}$ and the densities are of class $C^{m-1,1}$ for the single layer potential and of class $C^{m,1}$ for the double layer potential for some nonzero natural number $m$. The treatment of the limiting case requires generalized Schauder spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_11132 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A limiting case of a theorem of C. Miranda for layer potentials in Schauder spaces de Cristoforis, Massimo Lanza Analysis of PDEs 31B10, 35J25. 31B10, 35J25. 31B10, 35J25. 31B10, 35J25 The aim of this paper is to prove a theorem of C.~Miranda for the single and double layer potential corresponding to the fundamental solution of a second order differential operator with constant coefficients in Schauder spaces in the limiting case in which the open set is of class $C^{m,1}$ and the densities are of class $C^{m-1,1}$ for the single layer potential and of class $C^{m,1}$ for the double layer potential for some nonzero natural number $m$. The treatment of the limiting case requires generalized Schauder spaces. |
| title | A limiting case of a theorem of C. Miranda for layer potentials in Schauder spaces |
| topic | Analysis of PDEs 31B10, 35J25. 31B10, 35J25. 31B10, 35J25. 31B10, 35J25 |
| url | https://arxiv.org/abs/2409.11132 |